Question

Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

Step 1

To express the given connected sum (of surfaces) in the required form

Step 2

The connected sum of two surfaces X and Y (denoted by X#Y is the surface obtained by removing disks D and E from X and Y , attaching X-D and Y-E , identifying the boundaries of D and E. X#Y is well defined and does not depend on D and E.

Step 3

The operation # on the set of all connected surfaces is associative, commutatiive and has the sphere S2,

as...

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